Smooth actions of finite Oliver groups on spheres

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• 作者：Morimoto ; Masaharu ; Pawalowski ; Krzysztof
• 关键词：57S17 ; 57S25 ; 55M35 ; 55R35 ; 55R50 ; 55R91 ; 57R65 ; 57R67 ; Oliver group ; Gap group ; Smooth action on sphere ; Fixed point set ; Equivariant normal bundle ; Oliver obstruction ; Equivariant surgery ; Equivariant thickening ; Equivariant bundle extension ; Equivarian
• 刊名：Topology
• 出版年：2003
• 出版时间：March, 2003
• 年：2003
• 卷：42
• 期：2
• 页码：395-421
• 全文大小：262 K

文摘

In this article, we deal with the following two questions. For smooth actions of a given finite group G on spheres S, which smooth manifolds F occur as the fixed point sets in S, and which real G-vector bundles 57; over F occur as the equivariant normal bundles of F in S? We focus on the case G is an Oliver group and answer both questions under some conditions imposed on G, F, and 57;. We construct smooth actions of G on spheres by making use of equivariant surgery, equivariant thickening, and Oliver's equivariant bundle extension method modified by an equivariant wegde sum construction and an equivariant bundle subtraction procedure.